JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (12): 29-35.doi: 10.6040/j.issn.1671-9352.0.2016.078

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Existence and multiplicity of nontrivial solutions of Dirichlet problems for second-order impulsive differential equation

LI Xiao-yan, XU Man*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2016-02-27 Online:2016-12-20 Published:2016-12-20

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Abstract: In this paper, we study the existence and multiplicity of nontrivial solutions of Dirichlet problems for second-order impulsive differential equation{u″(t)+f(t,u(t))=0, t∈(0,1), t≠ti,Δu|t=ti=αiu(ti), i=1, 2,…,k,u(0)=u(1)=0,where αi>-1, i=1, 2,…,k are given constants, 0=t012<…kk+1=1 are given impulsive points. Δu|t=ti=u(t+i)-u(t-i), u(t+i), u(t-i) denote the right and left limit of u at t=ti, respectively. f∈C(［0,1］×R, R). The main results extend and improve some results on existence and multiplicity of nontrivial solutions of Dirichlet problems for second-order impulsive differential equation. The proof of the main results are based on the López-Gómezs bifurcation theory established in 2001.

Key words: second-order impulsive differential equation, bifurcation theory, nontrivial solutions

CLC Number: 

  • O175.8
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